Resonances of Cylindrical Shells with uniform radial pressure

I have picked up "Roark's Formulas for Stress and Strain" and "Mechanical Vibrations" and have been unable to reach resolution on a particular problem.

I am interested in the behavior of a uniform cylindrical shell (cylinder diameter >> wall thickness) rigidly clamped at both ends wherein uniform radial pressure is applied over the surface area of the cylinder.

How can I calculate the compliance and modal pattern of such an arrangement?